Chapter 4: Systems Based on Numbers

Section 6: Mathematical Functions

Differential equations [for sine sums]

The function Sin[x] + Sin[Sqrt[2] x] can be obtained as the solution of the differential equation y''[x] + 2 y[x] - Sin[x] 0 with the initial conditions y[0] 0, y'[0] 2.

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]